In the Milky Way, the distribution of stars in the $[\alpha/\mathrm{Fe}]$ vs. $[\mathrm{Fe/H}]$ and $[\mathrm{Fe/H}]$ vs. age planes holds essential information about the history of star formation, accretion, and dynamical evolution of the Galactic disk. We investigate these planes by applying novel statistical methods called copulas and elicitable maps to the ages and abundances of red giants in the APOGEE survey. We find that the low- and high-$\alpha$ disk stars have a clean separation in copula space and use this to provide an automated separation of the $\alpha$ sequences using a purely statistical approach. This separation reveals that the high-$\alpha$ disk ends at the same [$\alpha$/Fe] and age at high $[\mathrm{Fe/H}]$ as the low-$[\mathrm{Fe/H}]$ start of the low-$\alpha$ disk, thus supporting a sequential formation scenario for the high- and low-$\alpha$ disks. We then combine copulas with elicitable maps to precisely obtain the correlation between stellar age $\tau$ and metallicity $[\mathrm{Fe/H}]$ conditional on Galactocentric radius $R$ and height $z$ in the range $0 < R < 20$ kpc and $|z| < 2$ kpc. The resulting trends in the age-metallicity correlation with radius, height, and [$\alpha$/Fe] demonstrate a $\approx 0$ correlation wherever kinematically-cold orbits dominate, while the naively-expected negative correlation is present where kinematically-hot orbits dominate. This is consistent with the effects of spiral-driven radial migration, which must be strong enough to completely flatten the age-metallicity structure of the low-$\alpha$ disk.

翻译：在银河系中，恒星在 $[\alpha/\mathrm{Fe}]$ vs. $[\mathrm{Fe/H}]$ 以及 $[\mathrm{Fe/H}]$ vs. 年龄平面上的分布携带着关于银盘恒星形成、吸积和动力学演化历史的关键信息。我们通过应用名为copula和可映射图的新型统计方法，分析了APOGEE巡天中红巨星的年龄和丰度数据。研究发现，低α和高α银盘恒星在copula空间中呈现清晰分离，并据此利用纯统计方法实现了α序列的自动划分。这种分离揭示出高α银盘在高$[\mathrm{Fe/H}]$区域的终止点与低α银盘在低$[\mathrm{Fe/H}]$区域的起始点具有相同的[$\alpha$/Fe]值和年龄，从而支持了高、低α银盘依次形成的演化图景。我们进一步将copula与可映射图结合，精确获取了在银心距$R$（0 < $R$ < 20 kpc）和银面高度$z$（$|z|$ < 2 kpc）范围内，恒星年龄$\tau$与金属丰度$[\mathrm{Fe/H}]$的条件相关性。结果表明，年龄-金属丰度相关性随半径、高度和[$\alpha$/Fe]的变化趋势呈现显著特征：在运动学冷轨道占主导的区域相关性接近零，而运动学热轨道占主导的区域则表现出直觉预期的负相关。这一现象与旋臂驱动的径向迁移效应一致，且该效应必须足够强才能完全抹平低α银盘的年龄-金属丰度结构。